{"title": "Simulation of a Thalamocortical Circuit for Computing Directional Heading in the Rat", "book": "Advances in Neural Information Processing Systems", "page_first": 152, "page_last": 158, "abstract": "", "full_text": "Simulation of a Thalamocortical Circuit for \nComputing Directional Heading in the Rat \n\nHugh T. Blair* \n\nDepartment of Psychology \n\nYale University \n\nNew Haven, CT 06520-8205 \ntadb@minerva.cis.yale.edu \n\nAbstract \n\nSeveral  regions  of the  rat  brain  contain  neurons  known  as  head-direc(cid:173)\ntion celis,  which encode the animal's directional heading during spatial \nnavigation.  This  paper presents  a  biophysical  model of head-direction \ncell  acti vity,  which  suggests  that  a  thalamocortical  circuit  might com(cid:173)\npute the  rat's  head  direction  by  integrating  the  angular  velocity  of the \nhead over time.  The model was implemented using the neural simulator \nNEURON, and makes testable predictions about the structure and func(cid:173)\ntion of the rat head-direction circuit. \n\n1  HEAD-DIRECTION CELLS \nAs a rat navigates through space, neurons called head-direction celis encode the animal's \ndirectional  heading in the horizontal plane (Ranck,  1984; Taube, Muller, &  Ranck,  1990). \nHead-direction cells have been  recorded in  several  brain areas, including the postsubicu(cid:173)\nlum (Ranck,  1984) and anterior thalamus (Taube,  1995).  A  variety of theories  have pro(cid:173)\nposed  that  head-direction  cells  might  play  an  important  role  in  spatial  learning  and \nnavigation  (Brown  &  Sharp,  1995;  Burgess,  Recce,  &  O'Keefe,  1994;  McNaughton, \nKnierim, &  Wilson,  1995; Wan, Touretzky, &  Redish,  1994; Zhang,  1995). \n\n1.1  BASIC FIRING PROPERTIES \n\nA head-direction cell fires action potentials only when the rat's head is facing in a particu(cid:173)\nlar direction with respect to the static surrounding environment, regardless of the animal's \nlocation  within  that environment.  Head-direction cells are not influenced  by the position \nof the rat's head with respect to its body, they are only influenced by the direction of the \n\n*Also at the Yale Neuroengineering and Neuroscience Center (NNC), 5 Science Park North, New \n\nHaven, CT 06511 \n\n\fSimulation  of Thalamocortical  Circuit for Computing  Directional  Heading in  Rats \n\n153 \n\n,  0 \n\nG> \n~ \ng> \n~ 05 \n\n)( '\" E \n\n;! \n\n360,0 \n\n270 \n\n90 \n\no 0 0~~90~--:-::180:-\"--::27:70---~360 \n\nHead  Direction \n\n180 \n\nFigure  I:  Directional Tuning Curve of a Head-Direction Cell \n\nhead with respect to the stationary reference frame of the spatial environment.  Each head(cid:173)\ndirection cell  has  its  own directional  preference, so that together,  the entire population of \ncells can encode any direction that the animal is facing. \n\nFigure 1 shows an example of a head-direction cell's directional tuning curve, which plots \nthe firing  rate of the celI  as a function of the rat's momentary head direction.  The tuning \ncurve  shows  that  this  cell  fires  maximalIy  when  the  rat's  head  is  facing  in  a  preferred \ndirection  of about  160  degrees.  The  cell  fires  less  rapidly  for  directions  close  to  160 \ndegrees, and stops firing altogether for directions that are far from  160 degrees. \n\n1.2  THE VELOCITY INTEGRATION HYPOTHESIS \nMcNaughton, Chen, &  Markus (1991) have proposed that head-direction cells might rely \non  a process of dead-reckoning to  calculate the rat's current head direction,  based on the \nprevious  head  direction  and  the  angular  velocity  at  which  the  head  is  turning.  That  is, \nhead-direction cells might compute the directional position of the head by integrating the \nangular velocity of the head over time.  This velocity integration hypothesis is  supported \nby three experimental findings.  First, several brain regions that are associated with head(cid:173)\ndirection cells contain angular velocity cells, neurons that fire in proportion to the angular \nhead  velocity  (McNaughton  et al.,  1994;  Sharp,  in  press).  Second,  some head-direction \ncells in  postsubiculum are modulated by  angular head velocity, such that their peak firing \nrate  is  higher if the head  is  turning in  one direction than  in  the other (Taube et al.,  1990). \nThird, it has recently been found that head-direction cells in the anterior thalamus, but not \nthe postsubiculum, anticipate the future direction of the rat's head (Blair & Sharp,  1995). \n\n1.3  ANTICIPATORY HEAD-DIRECTION CELLS \n\nBlair and Sharp (1995) discovered that head-direction cells in  the anterior thalamus shift \ntheir directional preference to the left during clockwise turns, and to the right during coun(cid:173)\nterclockwise turns.  They showed that this shift occurs systematically as a function of head \nvelocity,  in  a way  that alIows  these cells anticipate the future  direction of the rat's  head. \nTo  illustrate  this,  consider a  cell  that  fires  whenever  the  head  will  be  facing  a  specific \ndirection, 9, in  the near future.  How would such a cell behave?  There are three cases to \nconsider.  First, imagine that the rat's head is turning clockwise, approaching the direction \n9 from  the left side.  In  this case, the anticipatory cell must fire when the head is facing  to \nthe left of 9, because being to the left of 9 and turning clockwise predicts arrival at 9 in the \nnear future.  Second, when  the head is turning counterclockwise and approaching 9 from \nthe right side, the anticipatory cell must fire when the head is to the right of 9.  Third, if the \nhead is still, then the cell should only fire  if the head is presently facing 9. \n\nIn  summary,  an  anticipatory  head direction  cell  should shift its  directional  preference to \nthe  left during clockwise turns,  to  the right during counterclockwise turns,  and  not at all \nwhen the head is still.  This behavior can be formalized by the equation \n\n!leV) = 9 - V't, \n\n[1] \n\n\f154 \n\nH. T.  BLAIR \n\nwhere ~ denotes the cell's preferred present head direction. v denotes the angular velocity \nof the head. 8 denotes the  future head direction that the cell anticipates, and 't is  a constant \ntime delay by  which the cell's activity anticipates arrival at 8.  Equation  1 assumes  that  ~ \nis  measured in degrees. which increase in the clockwise direction. and that v is positive for \nclockwise head turns. and negative for counterclockwise head turns.  Blair &  Sharp (1995) \nhave demonstrated  that  Equation  1 provides  a good  approximation of head-direction cell \nbehavior in  the  anterior thalamus. \n\n1.3  ANTICIPATORY TIME DELAY (r) \n\nInitial  reports  suggested  that  head-direction  cells  in  the  anterior thalamus  anticipate  the \nfuture head direction by an average time delay of't = 40 msec, whereas postsubicular cells \nencode  the  present  head  direction,  and  therefore  \"anticipate\"  by  't  = 0  msec  (Blair  & \nSharp,  1995; Taube &  Muller,  1995).  However, recent evidence suggests that individual \nneurons  in  the  anterior  thalamus  may  be  temporally  tuned  to  anticipate  the  rat's  future \nhead-direction  by  different time delays  between 0-100 msec, and  that postsubicular cells \nmay \"lag behind\" the present head-direction by about  to  msec (Blair &  Sharp,  1996). \n\n2  A BIOPHYSICAL MODEL \nThis section describes a biophysical model that accounts for the properties of head-direc(cid:173)\ntion  cells  in  postsubiculum  and  anterior thalamus.  by  proposing  that they  might be con(cid:173)\nnected to form  a thalamocortical circuit.  The next section presents simulation results from \nan implementation of the model, using the neural simulator NEURON (Hines,  1993). \n\n2.1  NEURAL ELEMENTS \n\nFigure 2 illustrates a basic circuit for computing the rat's head-direction.  The circuit con(cid:173)\nsists of five types of cells:  1)  Present Head-Direction (PHD) Cells encode the present \ndirection of the rat's head, 2) Anticipatory Head-Direction (AHD) Cells encode the future \ndirection of the rat's head, 3) Angular-Velocity (AV) Cells encode the angular velocity of \nthe rat's head (the CLK AV  Cell is active during clockwise turns, and the CNT AV Cell is \nactive during counterclockwise turns), 4) the Angular Speed (AS) Cell fires in inverse pro(cid:173)\nportion to the angular speed of the head, regardless of the turning direction (that is, the AS \nCell fires at a lower rate during fast turns, and at a higher rate during slow turns), 5) Angu(cid:173)\nlar-Velocity Modulated Head-Direction (AVHD) Cells are head-direction cells that fire \n\nAHDCells \n\nRTN  A~~~IS \n\n-\n\nExcitatory  ~ Inhibitory \n\n--~,;;\",I\".\u00b7 AS Cell  MB I \n\nABBREVIADONS \nAT = Anterior Thalamus \nMB. Mammillary Bodi .. \nPS = P08tsubiculum \nRS \u2022 Rempl\"'ill Cortex \nR1N = Reticul.11III. Nu. \n\nFigure 2:  A Model of the Rat Head-Direction System \n\n\fSimulation of Thalamocortical  Circuit for  Computing  Directional  Heading  in  Rats \n\n155 \n\nonly when the head is turning in one direction and not the other (the CLK AVHD Cell fires \nin  its  preferred  direction  only  when  the head  is  turning  clockwise,  and  the  CNT AVHD \nCell fires  in  its preferred direction only when the head turns counterclockwise). \n\n2.2  FUNCTIONAL CHARACTERISTICS \n\nIn  the  model,  AHD  Cells  directly  excite  their  neighbors  on  either  side,  but  indirectly \ninhibit these same  neighbors  via  the  AVHD  Cells,  which  act as  inhibitory  interneurons. \nAHD Cells also send excitatory feedback connections to themselves (omitted from Figure \n2 for clarity), so that once they become active. they remain active until they are turned off \nby  inhibitory  input (the  rate of firing  can also  be modulated by  inhibitory  input).  When \nthe  rat  is  not  turning  its  head.  the cell  representing  the current  head  direction  fires  con(cid:173)\nstantly, both exciting and inhibiting its neighbors.  In the steady-state condition (Le., when \nthe  rat is  not turning  its  head),  lateral  inhibition  exceeds  lateral  excitation,  and therefore \nactivity  does  not  spread  in  either direction  through  the  layer of AHD  Cells.  However. \nwhen  the  rat  begins  turning  its  head,  some of the  AVHD  Cells  are  turned off,  allowing \nactivity to  spread in  one direction.  For example. during a clockwise head tum. the CLK \nAV  Cell  becomes active,  and  inhibits  the  layer of CNT AVHD  Cells.  As a  result,  AHD \nCells stop inhibiting their right neighbors, so activity spreads to the right through the layer \nof AHD Cells.  Because AHD Cells continue to inhibit their neighbors to the left, activity \nis shut down in the leftward direction, in the wake of the activity spreading to the right. \n\nThe  speed  of propagation  through  the  AHD  layer is  governed  by  the AS  Cell.  During \nslow  head turns,  the AS  Cell  fires  at a  high  rate,  strongly  inhibiting the AHD Cells, and \nthereby  slowing the speed of propagation.  During fast  head turns,  the AS  Cell fires  at a \nlow  rate,  weakly inhibiting  the  AHD Cells,  allowing activity  to  propagate more quickly. \nBecause of inhibition from  AS  cells, AHD cells fire  faster when  the head is  turning  than \nwhen it is still (see Figure 4), in agreement with experimental data (Blair & Sharp,  1995). \n\nAHD Cells send a topographic projection to PHD Cells, such that each PHD Cell receives \nexcitatory  input from  an AHD  Cell that anticipates  when  the  head will soon be facing  in \nthe  PHD  Cell's  preferred  direction.  AHD  Cell  activity  anticipates  PHD  Cell  activity \nbecause there is  a transmission delay between the AHD and PHD Cells (assumed to  be 5 \nmsec  in  the  simulations  presented  below).  Also,  the  weights  of the  connections  from \nAHD Cells to PHD Cells are small, so each AHD Cell must fire  several action potentials \nbefore its  targeted PHD Cell  can  begin to  fire.  The time delay  between AHD and PHD \nCells accounts for anticipatory firing, and corresponds to the 1: parameter in Equation  I. \n\n2.3  ANATOMICAL CHARACTERISTICS \n\nEach component of the model  is  assumed to reside in  a specific  brain region.  AHD and \nPHD  Cells  are  assumed  to  reside  in  anterior  thalamus  (AT)  and  postsubiculum  (PS), \nrespectively.  AS Cells have been observed in PS (Sharp, in press) and retrosplenial cortex \n(RS) (McNaughton, Green, &  Mizumori,  1986), but the model predicts that they may also \nbe found  in the mammillary bodies (MB), since MB  receives input from  PS  and RS  (Shi(cid:173)\nbata,  1989), and  MB  projects to ATN.  AVHD Cells have  been observed in  PS  (Taube et \nai.,  1990),  but the  model  predicts  that they  may  aiso  be  found  in  the  reticular thalamic \nnucleus (RTN), because RTN receives input from PSIRS (Lozsadi, 1994), and RTN inhib(cid:173)\nits AT.  It should be noted that lateral excitation between ATN cells has not been shown, so \nthis feature of the model may be incorrect.  Table  1 summarizes anatomical evidence. \n\n3  SIMULATION RESULTS \nThe model illustrated in Figure 2 has been implemented using the neural simulator NEU(cid:173)\nRON (Hines.  1993).  Each neural element was represented as a single spherical compart-\n\n\f156 \n\nH.  T.  BLAIR \n\nTable  1:  Anatomical Features of the Model \n\nFEATURE OF MODEL \n\nREFERENCE \n\nPHD Cells in PSIRS \nAHD Cells in  AT \nAV Cells in PSIRS \nAT projects to PS \nAT projects to RTN \nPSIRS projects to RTN \nAVHD Cells in RTN \nAS Cells in MB \n\nChen et aI.,  1990; Ranck,  1984 \nBlair &  Sharp,  1995 \nMcNaughton et aI., 1994; Sharp, in press \nvan Groen &  Wyss,  1990 \nShibata,  1992 \nLozsadi,  1994 \nPREDICTION OF MODEL \nPREDICTION OF MODEL \n\nment, 30 Jlm in diameter,  with RC time constants ranging between  15 and 30 msec.  Syn(cid:173)\naptic  connections  were  simulated  using  triggered  alpha-function  conductances.  The \nresults presented here demonstrate the behavior of the model, and compare the properties \nof the model with experimental data. \n\nTo begin each simulation, a small current was injected in to one of the AHD Cells, causing \nit to  initiate sustained firing.  This cell  represented the simulated rat's  initial  head direc(cid:173)\ntion.  Head-turning behavior was simulated by injecting current into the AV and AS  Cells, \nwith an amplitude that yielded firing proportional to the desired angular head velocity. \n\n3.1  ACTIVITY OF HEAD-DIRECTION CELLS \n\nFigure  3  presents  a  simple  simulation,  which  illustrates  the  behavior of head-direction \ncells in the model.  The simulated rat begins by facing in the direction of 0 degrees.  Over \nthe  course of 250  msec,  the  rat quickly  turns  its  head  60 degrees  to  the  right,  and  then \nreturns to the initial starting position of 0 degrees.  The average velocity of the head in this \nsimulation  was 480 degrees/sec,  which is  similar to the speed at which an actual  rat per(cid:173)\nforms  a fast  head tum  (Blair &  Sharp,  1995).  Over the course of the simulation,  neural \nactivation propagates from  the O-degree cell to the 60-degree cell, and then back to the 0-\ndegree cell. \n\n3.2  COMPARISON WITH EXPERIMENTAL DATA \n\nTo examine how  well  the model reproduces firing  properties of PS  and AT cells, another \nsimple simulation  was  performed.  The firing  rate the model's PHD and AHD Cells  was \nexamined  while  the  simulated  rat performed  several  360-degree revolutions  in  both  the \nclockwise and counterclockwise directions.  Results are summarized in Figure 4, which \n\nACTIVITY OF PHD CELLS \n\nANIMAL \nBEHAVIOR \n\n15-\nc.lll_WlM\"-__ -----\"'~~ \n30-\nCelII----MMIM'-_--M\\.W~ \noW \nCelII----~~ ___ -M~~ \n60-\nc.III=:::;~~~~~:::;::==::, \n\n, \n\n50 \n\n100 \nTurning Right \n\n1 \n\nA'--;Tu....,mIng~Le~1t ---:, \n\nTime (msec) \n\nWSOIIIt \n\n\u2022\u2022.......... \n\n\". \n\nAVlrlgl Angular Velocity = 480\" 'sec \n\nFigure 3: Simulation Example \n\n\fSimulation of Thalamocortical  Circuit  for  Computing Directional  Heading  in  Rats \n\n157 \n\n. n \n\n.\u2022\u2022\u2022\u2022\u2022 \n\nN'25.0  r - ,  --~-----\n\nO<>\"T (exper.,..ntaI Getal \n0-0 Ps (.)(~'\"*\"\". ,*a) \n_AT (modol dolo ' \n. .  Ps (model ~. ) \n\n\u2022\u2022\u2022\u2022\u2022 \n\no.-/' ..... \u00b7\u00b7\u00b7\u00b7\u00b7~ \n\n~ \n\nCil12.0  - -- - - - - - - - . ,  \n~ 10.0  . \nZ' ~ 8.0 ' \nCD \n15\u00bb \n.:i  40 : \ng  2.0  i \n,;  0.0  i \nio \nN  0 \nFigure 4: Compared Properties of Real and Simulated Head-Direction Cells \n\ne. \n~ 20.0  ~ \n.= Li:  10.0  , \n0)15.0  , \ng, \nI \nCii  5.0 , \n~ 0.0  i~ _______ -' \n500 \nAngular Head Velocity (degJsec) \n\n500 \nAngular Head Velocity (deglsec) \n\n[} ...\u2022..........\u2022.\u2022....\u2022 -o \n\u2022 \n\u2022 \n-----' \n\n\u2022 \n[}----------------.----.-o \n\n_\n200  300 \n\n_ \n400 \n\n.2.0  ,'--_ ___\n\n6.0  I \n\n100 \n\no \n\n100 \n\n200 \n\n300 \n\n400 \n\ncompares  simulation  data  with  experimental  data.  The  experimental  data  in  Figure  4 \nshows averaged results for 21  cells recorded in AT, and 19 cells recorded in PS. \n\nBecause AT  cells  anticipate the future  head direction,  they exhibit an  angular separation \nbetween their clockwise and counterclockwise directiQnal preference, whereas as no  such \nseparation occurs for PS cells (see section 2.4).  For AT cells, the magnitude of the angular \nseparation  is  proportional  to  angular head  velocity,  with greater separation occurring  for \nfast turns, and less separation for slow turns (see Eq.  1).  The left panel of Figure 4 shows \nthat the model's PHD and AHD Cells exhibit a similar pattern of angular separation. \n\nBlair &  Sharp (1995) reported that the firing  rates of AT  and PS  cells differ in  two ways: \n1) AT cells fire at a higher rate than PS cells, and 2) AT cells have a higher rate during fast \nturns  than during slow turns, whereas PS cells fire  at the same rate,  regardless of turning \nspeed.  In Figure 4 (right panel), it can be seen that the model reproduces these findings. \n\n4  DISCUSSION AND CONCLUSIONS \nIn this paper, I have presented a neural model of the rat head-direction system.  The model \nincludes neural elements  whose firing  properties are similar to  those of actual  neurons  in \nthe rat brain.  The model suggests that a thalamocortical circuit might compute the direc(cid:173)\ntional position of the rat's head, by integrating angular head velocity over time. \n\n4.1 COMPARISON WITH OTHER MODELS \n\nMcNaughton  et  al.  (1991)  proposed  that  neurons  encoding  head-direction  and  angular \nvelocity might be connected to form  a linear associative mapping network.  Skaggs et  al. \n(1995)  have refined this  idea into a theoretical circuit, which  incorporates head-direction \nand angular velocity cells.  However, the Skaggs et al.  (1995) circuit does not incorporate \nanticipatory  head-direction cells,  like those found  in  AT.  A model  that does incorporate \nanticipatory cells has  been developed  by  Elga, Redish,  &  Touretzky  (unpublished manu(cid:173)\nscript).  Zhang  (1995)  has recently presented a theoretical analysis of the head-direction \ncircuit, which suggests that anticipatory head-direction cells might be influenced by  both \nthe angular velocity and  angular acceleration of the head,  whereas non-anticipatory cells \nmay be influenced by the angular velocity only, and not the angular acceleration. \n\n4.2  LIMITATIONS OF THE MODEL \n\nIn its current form,  the model suffers some significant limitations.  For example, the direc(cid:173)\ntional  tuning  curves of the model's  head-direction cells are much narrower than those of \nactual  head-direction  cells.  Also,  in  its present form, the model  can accurately track the \nrat's head-direction over a rather limited range of angular head velocities.  These limita(cid:173)\ntions are presently being addressed in a more advanced version of the model. \n\n\f158 \n\nAcknowledgments \n\nH. T.  BLAIR \n\nThis  work  was  supported  by  NRSA  fellowship  number  1  F31  MH11102-01Al  from \nNIMH.  a  Yale  Fellowship.  and  the  Yale  Neuroengineering  and  Neuroscience  Center \n(NNC).  I thank Michael Hines. Patricia Sharp. and Steve Fisher for their assistance. \n\nReferences \nBlair.  H.T ..  & Sharp. P.E.  (1995).  Anticipatory  head-direction cells  in  anterior thalamus: \nEvidence for a thalamocortical circuit that mtegrates angular head velocity to compute \nhead direction. Journal of Neuroscience,  IS,  6260-6270. \n\nBlair, H.T .\u2022  & Sharp (1996). Temporal Tuning of Anticipatory Head-Direction Cells in the \n\nAnterior Thalamus of the Rat. Submitted. \n\nBrown. M.  &  Sharp. P.E.  (1995). Simulation of spatial learning in  the morris water maze \nby  a.  neural  network  model  of the  hippocampal  formation  and  nucleus  accumbens. \nHippocampus,  5.  171-188. \n\nBurgess, N .\u2022  Recce.  M .\u2022 & O'Keefe. J.  (1994).  A model of hippocampal function.  Neural \n\nNetworks,  7.  1065-1081. \n\nsystem. Unyublished Manuscript. \n\nElga. AN .\u2022  Redish, AD .\u2022  &  Touretzky. D.S. (1995). A model of the rodent head-direction \n\nHines. M.  (1993). NEURON: A program for simulation of nerve equations. In F.  Eckman \n\n(Ed.). Neural Systems: Analysis and Modeling,  Norwell. MA : Kluwer Academic Pub(cid:173)\nlishers. pp.  127-136. \n\nLozsadi. D.A. (1994). Organization of cortical afferents to the rostral, limbic sector of the \n\nrat thalamic reticular nucleus. The Journal of Comparative Neurology,  341, 520-533. \nMcNaughton. B.L.. Chen. L.L.. & Markus. E.1.  (1991).  Dead reckoning, landmark learn(cid:173)\n\ning.  and  the  sense of direction:  a  neurophysiological  and computational  hypothesis. \nJournal of Cognitive Neuroscience,  3,  190-202. \n\nMcNaughton,  B.L..  Green.  E.1 .\u2022  &  Mizumori,  S.1.y.  (1986).  Representation  of  body \nmotion  trajectory  by  rat  sensory  motor  cortex  neurons.  Society  for  Neuroscience \nAbstracts.  12,260. \n\nMcNaughton, B.L.. Knierim. J.J .\u2022  & Wilson. M.A (1995). Vector encoding and the vestib(cid:173)\nular  foundations  of spatial  cognition:  neurophysiological  and computational  mecha(cid:173)\nnisms. In M. Gazzaniga (Ed.). The Cognitive Neurosciences. Cambndge: MIT Press. \n\nMcNaughton. B.L.. Mizumori, S.Y.1 .\u2022 Barnes. C.A .\u2022  Leonard. B.J .\u2022  MarqUiS. M .\u2022  & Green. \nB.J. (1994). Coritcal representation of motion during unrestrained spatial navigaton in \nthe rat. Cerebral Cortex,  4,  27-39. \n\nRanck, J.B. (1984).  Head-direction cells in the deep ceUlayers of dorsal presubiculum in \n\nfreely moving rats. Society for Neuroscience Abstracts, 12,  1524. \n\nShibata. H. (1989). Descending projections to the mammillary nuclei in the rat. as studied \nby retrograde and anterograde transport of wheat germ agglutinin-horseradish peroxi(cid:173)\ndase. The Journal of Comparative Neurology,  285. 436-452. \n\nShibata. H.  (1992). Topographic organization of subcortical projections to the anterior tha(cid:173)\n\nlamic nuclei in the rat.  The Journal of Comparative Neurology,  323,  117-127. \n\nSharp, P.E.  (in press). Multiple spatiallbehavioral corrrelates for cells in the rat postsubic(cid:173)\nulum:  multiple regression analysis and comparison to other hippocampal areas.  Cere(cid:173)\nbral Cortex. \n\nSkaggs,  W.E .\u2022  Knierim.  J.1 .\u2022  Kudrimoti.  H.S.,  &  McNaughton,  B.L.  (1995).  A  model  of \nthe  neural  basis of the rat's sense of direction.  In  G.  Tesauro. D.S.  Touretzky,  & T.K. \nLeen (Eds.), Advances in Neural Information Processing Systems 7.  MIT Press. \n\nTaube. 1.S. (1995). Head-direction cells recorded in the anterior thalamic nuclei of freely(cid:173)\n\nmoving rats. Journal of Neuroscience,  15, 70-86. \n\nTaube. J.S .\u2022  & Muller. R.O.  (1995).  Head-direction cell activity  in  the anterior thalamus. \nbut not the postsubiculum, predicts the animal's future directional heading. Society for \nNeuroscience Abstracts. 21. 946. \n\nTaube.  J.S.,  Muller.  R.U .\u2022  & Ranck, J.B.  (1990). Head-direction cells recorded  from  the \npostsubiculum in freely  moving rats,  I.  Description and quantitative analysis. Jounral \nof Neuroscience,  10,  420-435. \n\nvan Groen. T.,  & Wyss, J.M.  (1990). The postsubicular cortex  in  the rat:  characterization \nof the fourth  region of subicular cortex and its connections.  Journal of Comparative \nNeurology, 216.  192-210. \n\nWan,  H.S .\u2022  Touretzky. D.S .\u2022  & Redish. D.S. (1994). A rodent navigation model that com(cid:173)\nbines place code. head-direction, and path integration information. Society for Neuro(cid:173)\nscience Abstracts, 20,  1205. \n\nZhang,  K.  (1995).  Representation  of spatial  orientation  by  the  intrinsic  dynamics of the \n\nhead-direction cell ensemble: A theory.  Submitted. \n\n\f", "award": [], "sourceid": 1129, "authors": [{"given_name": "Hugh", "family_name": "Blair", "institution": null}]}